RTT analyses

This notebook contains the analyses performed for the "Evaluating Wi-Fi Round Trip Time for Accurate Indoor Positioning with Android Smartphones" conference paper.

The contained analyses are:

1. Temporal variability or RTT measures.
2. Impact of the angle of incidence (AoI).
3. RTT sampling interval limitations.
4. Variability of RTT measures from multiple emitters in several reference locations.

Imports

import os
import numpy as np
import pandas as pd
import plotly.express as px
import plotly.graph_objects as go

from PIL import Image
from plotly.subplots import make_subplots

INPUT_DATA_DIR = '01_DATA'
POCO_MEASUREMENTS = os.path.join(INPUT_DATA_DIR, '01_rtt-poco.csv')
M2007_MEASUREMENTS = os.path.join(INPUT_DATA_DIR, '01_rtt-xiaomi-m2007.csv')
ORIENTATIONS_MEASURMENTS = os.path.join(INPUT_DATA_DIR, '02_rtt-orientations.csv')
THROTTLE_MEASURMENTS = os.path.join(INPUT_DATA_DIR, '03_rtt-throttle.csv')
MULTIPLE_EMITTERS_MEASUREMENTS = {
    'P1': os.path.join(INPUT_DATA_DIR, '04_P1-rtt.csv'),
    'P2': os.path.join(INPUT_DATA_DIR, '04_P2-rtt.csv'),
    'P3': os.path.join(INPUT_DATA_DIR, '04_P3-rtt.csv')
}
FLOORMAP = os.path.join(INPUT_DATA_DIR, '04_basemap.jpg')

RESULTS_DATA_DIR = '02_RESULTS'
TEMPORAL_VARIABILITY_POCO = os.path.join(RESULTS_DATA_DIR, '01_rtt-variability-poco.pdf')
TEMPORAL_VARIABILITY_M2007 = os.path.join(RESULTS_DATA_DIR, '01_rtt-variability-m2007.pdf')
ORIENTATIONS_RESULTS = os.path.join(RESULTS_DATA_DIR, '02_rtt-orientations.pdf')
THROTTLE_RESULTS = os.path.join(RESULTS_DATA_DIR, '03_rtt-throttle.pdf')
MULTIPLE_EMITTERS_COLLECTION_ENV = os.path.join(INPUT_DATA_DIR, '04_collection-environment.jpg')
MULTIPLE_EMITTERS_ERRORS_FIG = os.path.join(RESULTS_DATA_DIR, '04_rtt-multiple-emitters.pdf')
MULTIPLE_EMITTERS_ERRORS_TABLE = os.path.join(RESULTS_DATA_DIR, '04_rtt-multiple-emitters.csv')

REFERENCE_LOCATIONS = {
    'P1': [3.91, 7.76],
    'P2': [4, 2.10],
    'P3': [1.19, 14.14],
}

APS_LOCATIONS = {
    '90:ca:fa:8b:13:b4': (4.0, 1.10),
    '90:ca:fa:8b:26:29': (0.21, 1.17),
    '24:e5:0f:2c:ff:15': (4.84, 14.65),
    '24:e5:0f:2d:13:79': (0.17, 14.74)
}

APS_IDS = {
    '90:ca:fa:8b:13:b4': 'AP1',
    '90:ca:fa:8b:26:29': 'AP2',
    '24:e5:0f:2c:ff:15': 'AP3',
    '24:e5:0f:2d:13:79': 'AP4'
}

LAB_WIDTH = 6.34
LAB_HEIGHT = 14.94

HEIGHT = 500
WIDTH = 700

FONT_SIZE = 18

Analysis

Temporal variability of RTT measures

Analysis of the temporal evolution and accuracy of RTT measurements collected at 1000, 2000, 3000, 4000 and 5000 millimeters from the AP. The data was collected with two Android smartphones and locations: Xiaomi Poco F2 Pro (M2004J11G) in a research laboratory and a Xiaomi Mi 10T (M2007J3SG) in an urban home.

Data loading

poco = pd.read_csv(POCO_MEASUREMENTS)
m2007 = pd.read_csv(M2007_MEASUREMENTS)
poco = poco[poco['Real Distance (mm)'].isin([1000, 2000, 3000, 4000, 5000])]
poco['Real Distance (mm)'] = poco['Real Distance (mm)'].astype(str)
m2007['Real Distance (mm)'] = m2007['Real Distance (mm)'].astype(str)

Results

poco_fig = px.scatter(poco, x='Time (ms)', y='Distance (mm)', color='Real Distance (mm)')

poco_fig.update_layout(width=WIDTH, height=HEIGHT, 
    legend=dict(
        yanchor="top",
        y=0.99,
        xanchor="left",
        x=0.01,
        orientation='h'
    ), yaxis_range=[1000, 9000], xaxis_title_font_size=FONT_SIZE, yaxis_title_font_size=FONT_SIZE)

m2007_fig = px.scatter(m2007, x='Time (ms)', y='Distance (mm)', color='Real Distance (mm)')

m2007_fig.update_layout(width=WIDTH, height=HEIGHT, 
    legend=dict(
        yanchor="top",
        y=0.99,
        xanchor="left",
        x=0.01,
        orientation='h'
    ), yaxis_range=[1000, 9000], xaxis_title_font_size=FONT_SIZE, yaxis_title_font_size=FONT_SIZE)

Impact of the Angle of Incidence (AoI)

Analysis of the orientation of the smartphone with respect to the AP. The RTT measurements were collected at 0.5 meters from the AP with the Xiaomi Poco F2 Pro (M2004J11G) in a research laboratory.

Data loading

orientations = pd.read_csv(ORIENTATIONS_MEASURMENTS)
orientations['Orientation'] = orientations['Orientation'].map({1: 'A', 2: 'B', 3: 'C', 4: 'D', 5: 'E'})

Results

orientation_fig = px.box(orientations, x='Orientation', y='Distance (mm)', points="all", color='Orientation')

orientation_fig.update_layout(
    height=HEIGHT,
    width=WIDTH,
    showlegend=False, 
    xaxis_title_font_size=FONT_SIZE, 
    yaxis_title_font_size=FONT_SIZE
)

RTT sampling interval limitations

Analysis of the quantity of RTT measurments received with several sampling interval configurations.

Data loading

throttle = pd.read_csv(THROTTLE_MEASURMENTS)
throttle['Interval (ms)'] = throttle['Interval (ms)'] * -1

Results

throttle_fig = make_subplots(specs=[[{"secondary_y": True}]])

throttle_fig.add_trace(
    go.Scatter(x=throttle['Interval (ms)'], y=throttle['Successful Measurements'], name="N. of successfull RTT ops."),
    secondary_y=False,
)

throttle_fig.add_trace(
    go.Scatter(x=throttle['Interval (ms)'], y=throttle['% Successful Operations'], line_dash='dashdot', name="% of successful RTT ops."),
    secondary_y=True,
)

throttle_fig.update_layout(height=HEIGHT, width=WIDTH + 100,
    legend=dict(
        orientation="h",
        yanchor="bottom",
        y=1.02,
        xanchor="right",
        x=0.94,
        bordercolor="Black",
        borderwidth=2
    ))
throttle_fig.update_xaxes(title_text="Sampling interval (ms)", title_font_size=FONT_SIZE, autorange='reversed', dtick=50)
throttle_fig.update_yaxes(title_text="RTT Operations", title_font_size=FONT_SIZE, secondary_y=False, dtick=50)
throttle_fig.update_yaxes(title_text="Success rate (%)", title_font_size=FONT_SIZE, secondary_y=True, griddash='dashdot', gridcolor='black')

Variability of RTT measures from multiple emitters in several reference locations

Analysis of accuracy of RTT measurements collected at three reference points from four AP deployed in the research laboratory. The RTT measurements were collected with the Xiaomi Poco F2 Pro (M2004J11G).

Data collection environment

SYMBOLS = {
    'AP1': 'triangle-right',
    'AP2': 'triangle-right',
    'AP3': 'triangle-left',
    'AP4': 'triangle-left',
}

def plot_collection_environment():
    fig=go.Figure()
    fig = add_reference_points(fig)
    fig = add_aps(fig)
    fig = add_floorplan(fig)
    fig = add_style(fig)
    return fig


def add_reference_points(fig):
    points_identifiers = list(REFERENCE_LOCATIONS.keys())
    points_x = [location[1] for location in REFERENCE_LOCATIONS.values()]
    points_y = [location[0] for location in REFERENCE_LOCATIONS.values()]
    fig.add_trace(
        go.Scatter(
            x=points_x, y=points_y, name="Reference points", legendgroup='1',
            mode='markers+text', marker_size=18, marker_color='red', marker_line_width=2,
            text=points_identifiers, texttemplate="<b>%{text}</b>", textposition="top center", textfont_color='red', textfont_size=14
        )
    )
    return fig


def add_aps(fig):
    aps_x = [ap[1] for ap in APS_LOCATIONS.values()]
    aps_y = [ap[0] for ap in APS_LOCATIONS.values()]
    aps_identifiers = [APS_IDS[ap_id] for ap_id in APS_LOCATIONS.keys()]
    fig.add_trace(
        go.Scatter(
            x=aps_x, y=aps_y, name='APs', mode='markers+text',  
            marker=dict(symbol=[SYMBOLS[identifier] for identifier in aps_identifiers],
                        opacity=1, color='green', size=18, line=dict(width=2)), 
            text=aps_identifiers, texttemplate="<b>%{text}</b>", textposition='top left', textfont_color='green', textfont_size=14
        )
    )
    return fig


def add_floorplan(fig):
    fig.add_layout_image(
        dict(
            source=Image.open(FLOORMAP),
            xref="x", x=0, xanchor="left", sizey=LAB_WIDTH,
            yref="y", y=0, yanchor='top', sizex=LAB_HEIGHT,
            sizing="stretch",
            opacity=1,
            layer="below"
        )
    )
    return fig


def add_style(fig):
    fig.update_layout(
        width=750, height=HEIGHT, plot_bgcolor='white', 
        legend=dict(orientation="h", yanchor="bottom", y=1, xanchor="right", x=1),
    )
    fig.update_xaxes(showgrid=False, showticklabels=False, tickmode="linear", range=[0, 15])
    fig.update_yaxes(showgrid=False, showticklabels=False, tickmode="linear", range=[6.5, 0], scaleanchor="x", scaleratio=1)
    return fig


collection_env = plot_collection_environment()
collection_env

Data loading

def load_multiple_ap_measurements():
    dfs = []
    for reference_location, measurements_file in MULTIPLE_EMITTERS_MEASUREMENTS.items():            
        measurements = pd.read_csv(measurements_file)
        measurements['Reference Position'] = reference_location
        measurements['AP'] = measurements['AP MAC Address'].apply(lambda x: APS_IDS[x])
        measurements['Real Distance (mm)'] = measurements['AP MAC Address'].apply(lambda x: euclidean_distance(*REFERENCE_LOCATIONS[reference_location], *APS_LOCATIONS[x]) * 1000)
        measurements['Error (mm)'] = measurements['Distance (mm)'] - measurements['Real Distance (mm)']
        dfs.append(measurements)
    return pd.concat(dfs).sort_values(['Reference Position', 'AP'])


def euclidean_distance(x1, y1, x2, y2):
    p1 = np.array((x1 ,y1))
    p2 = np.array((x2, y2))
    return np.linalg.norm(p1 - p2)


multiple_emitters = load_multiple_ap_measurements()

Results

multiple_emitters_fig = px.box(multiple_emitters, y='Distance (mm)', x='Reference Position', color='AP', points='all', width=WIDTH*2, height=HEIGHT)
multiple_emitters_fig.update_layout(
    xaxis_title_font_size=FONT_SIZE, yaxis_title_font_size=FONT_SIZE,
    legend=dict(yanchor="top", y=0.95, xanchor="right", x=0.99),
    yaxis_range=[0, 23000], yaxis_dtick=1000, yaxis_ticklabelstep=5)

multiple_emitters_fig

errors_by_ap_and_position = multiple_emitters[['Distance (mm)', 'Real Distance (mm)', 'Reference Position', 'AP']].groupby(['Reference Position', 'AP']).mean()
errors_by_ap_and_position['Error'] = errors_by_ap_and_position['Distance (mm)'] - errors_by_ap_and_position['Real Distance (mm)']
errors_by_ap_and_position

		Distance (mm)	Real Distance (mm)	Error
Reference Position	AP
P1	AP1	8318.357843	6660.608080	1657.749763
	AP2	9577.049020	7557.651752	2019.397268
	AP3	8443.575610	6952.481571	1491.094038
	AP4	10037.382353	7918.838299	2118.544054
P2	AP1	2545.420290	1000.000000	1545.420290
	AP2	6219.666667	3902.435137	2317.231529
	AP3	14821.420290	12578.080140	2243.340150
	AP4	19260.666667	13207.516799	6053.149868
P3	AP1	16845.133663	13339.329069	3505.804595
	AP2	16759.618812	13006.971208	3752.647604
	AP3	4418.217822	3685.457909	732.759913
	AP4	3666.490099	1183.384975	2483.105124

Storing results

poco_fig.write_image(TEMPORAL_VARIABILITY_POCO)
m2007_fig.write_image(TEMPORAL_VARIABILITY_M2007)
orientation_fig.write_image(ORIENTATIONS_RESULTS)
throttle_fig.write_image(THROTTLE_RESULTS)
collection_env.write_image(MULTIPLE_EMITTERS_COLLECTION_ENV)
multiple_emitters_fig.write_image(MULTIPLE_EMITTERS_ERRORS_FIG)
errors_by_ap_and_position.to_csv(MULTIPLE_EMITTERS_ERRORS_TABLE)